Finding Partial Sums in a Series

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Math › Finding Partial Sums in a Series

Questions 1 - 3

1

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

$S=\frac{30}{2}(2+60)=15(62)=930$

2

Find the sum of the even integers from to .

Explanation

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where is the first value in the series, is the number of terms, and is the difference between sequential terms.

Plugging in our values, we get:

$S = \frac{51}{2}(2(250)+(51-1)2)$

3

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

We know that there are terms in the series. The first term is and the last term is . Our formula becomes:

$S = \frac{50}{2}(250+350)$

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